How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ?

Correct Answer: 9944

Explanation:

To find the largest 4 digit number exactly divisible by 88,

We should divide the largest possible 4 digit number by 88, and if we get any remainder than subtract it from that largest number.

The largest possible 4 digit number is 9999

Now,

 

88) 9999 (113
      88
  _______
      119
        88
  _______
        319
        264
  _______
          55
  _______

 

Therefore, the largest 4 digit number exactly divisible by 88 is given by

9999 - 55 = 9944.

Correct Answer: 42437

Explanation:

The square of a natural number never ends in 7.
42437 is not the square of a natural number

Correct Answer: 222

Correct Answer: 8 and 5

Explanation:

Let the number  be 476ab0 

 

476ab0 is divisible by 3 

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

 

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11  --------------(ii)

 

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

 

if a=6 and b=2, 

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

 

if a=8 and b=2, 

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

 

if a=6 and b=5, 

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

 

 

if a=8 and b=5, 

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer

Correct Answer: 4964

Explanation:

The pattern is  1 2 2 2 , 3 2 4 2 , 5 2 6 2, 

?The next number= 7 2 8 2= 4964

Correct Answer: ¹²⁄₃₅

Explanation:

Let the numbers be a and b . Then, a + b = 12 and ab = 35.

∴	a + b	=	12	⟹	❨	1	+	1	❩	=	12
	ab		35			b		a			35

∴ Sum of reciprocals of given numbers =	12
	35

Correct Answer: 9

Correct Answer: 2

Explanation:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x ), which must be divisible by 3.

∴  x = 2.

Correct Answer: 60

Explanation:

Let,

no. of rice bowl = x
no. of dal bowl = y
no. of meat bowl = z

Then, x + y + z = 65 ....(1)

Also given that, 2x = 3y = 4z

substituting value of y & z in terms of x i.e. y = 2x/3 and z = x/2 in eq (1),
We get x = 30.

As 1 rice bowl is shared between 2 guests,
Therefore, there are 60 guests.

Correct Answer: 17

Explanation:

The pattern is  3 2 + 4 2 = 5 2,   5 2 + 12 2 = 13 2,  7 2 + 24 2 = 25 2 

The next number =  8 2 + 15 2 = 17 2

 i.e. 17